We give an improved quantitative version of the Kendall theorem. The Kendall theorem states that under mild conditions imposed on a probability distribution on the positive integers (i.e. a probability sequence) one can prove convergence of its renewal sequence. Due to the well-known property (the first entrance last exit decomposition) such results are of interest in the stability theory of time-homogeneous Markov chains. In particular this approach may be used to measure rates of convergence of geometrically ergodic Markov chains and consequently implies estimates on convergence of MCMC estimators.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am40-2-1,
author = {Witold Bednorz},
title = {The Kendall theorem and its application to the geometric ergodicity of Markov chains},
journal = {Applicationes Mathematicae},
volume = {40},
year = {2013},
pages = {129-165},
zbl = {1274.60237},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-2-1}
}
Witold Bednorz. The Kendall theorem and its application to the geometric ergodicity of Markov chains. Applicationes Mathematicae, Tome 40 (2013) pp. 129-165. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-2-1/